Mathematics · JEE | INTEGRALS
हिन्दीMatch List-I with List-II: List-I List-II A \( \int \tan x \, dx \) I \( \log |\sin x| + C \) B \( \int \cot x \, dx \) II \( \log |\sec x + \tan x| + C \) C \( \int \sec x \, dx \) III \( \log |\sec x| + C \) D \( \int \operatorname{cosec} x \, dx \) IV \( \log |\operatorname{cosec} x - \cot x| + C \) Choose the correct answer from the options given below:
Match List-I with List-II:
| List-I | List-II | ||
|---|---|---|---|
| A | \( \int \tan x \, dx \) | I | \( \log |\sin x| + C \) |
| B | \( \int \cot x \, dx \) | II | \( \log |\sec x + \tan x| + C \) |
| C | \( \int \sec x \, dx \) | III | \( \log |\sec x| + C \) |
| D | \( \int \operatorname{cosec} x \, dx \) | IV | \( \log |\operatorname{cosec} x - \cot x| + C \) |
Choose the correct answer from the options given below:
View Answer & Solution
Correct answer · Option D
A-(III), B-(I), C-(II), D-(IV)
Explanation
Standard logarithmic integrations of basic trigonometric functions give \( \int \tan x dx = \log|\sec x|+C \), \( \int \cot x dx = \log|\sin x|+C \), \( \int \sec x dx = \log|\sec x + \tan x|+C \), and \( \int \operatorname{cosec} x dx = \log|\operatorname{cosec} x - \cot x|+C \).